MGF 1106 Final Exam Review 9) {5} D 10) D B 11) U

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1 MGF 1106 Final Exam Review Use inductive reasoning to predict the next number in the sequence. 1) 7, -14, 28, -56, 112 Find n(a) for the set. 2) A = { 3, 5, 7, 9, 11} Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. Determine the following. 3) A B' 4) A (B C) 5) n(a B) Tell whether the statement is true or false. If false, give the reason. 6) 10 { 20, 30, 40, 50, 60} Use the Venn diagram shown to list the set in roster form. Let U = {1, 2, 3, 4, 5, 6, 7, 8} A = {1, 3, 5, 7} B = {5, 6, 7, 8} C = {5, 8} D = {2, 5, 8} Determine whether the statement is true or false. 9) {5} D 10) D B 11) U 12) Mrs. Bollo's second grade class of thirty students conducted a pet ownership survey. Results of the survey indicate that 8 students own a cat, 15 students own a dog, and 5 students own both a cat and a dog. How many of the students surveyed own no cats? 13) A group of 180 6th graders was given the option to play three sports. These were soccer, kickball, and basketball. They chose sports as follows: 85 played soccer 72 played kickball 73 played basketball 29 played both soccer and kickball 32 played kickball and basketball 43 played soccer and basketball 12 played all three sports a. How many played only one sport? b. How many chose not to play any of these sports? 7) A C Use,,, or both and to make a true statement. 8) {a, b} {z, a, y, b, x, c} Write a negation of the statement. 14) Some athletes are musicians. 15) Some people don't like walking. Determine whether the two statements are equivalent. 16) ~(~p q), p ~q 17) ~(p q) r, (~p ~q) r Write the converse, inverse, and contrapositive of the given statement. 18) If you like me, then I like you.

2 Determine which, if any, of the three statements are equivalent. 19) I) If tomorrow is not Monday, then today is not Sunday. II) Today is not Sunday and tomorrow is not Monday. III) It is not the case that today is Sunday and tomorrow is Monday. Choose the statement which is equivalent to If I don t have a hammer, then I can hammer in the morning. 20) i. If I have a hammer, then I cannot hammer in the morning ii. If I hammer in the morning, then I have a hammer. Determine whether each of the following is true or false. 25) i. The intersection between two lines may be a ray. ii. The union of a line segment and a ray may be a ray. iii. The intersection of two rays may be a line segment. iv. The union of two rays may be a point. Use the figure to find the following. 26) iii. If I can t hammer in the morning, then I have a hammer. iv. If I can t hammer in the morning, then I don t have a hammer. Given p is true, q is true, and r is false, find the truth value of the statement. 21) (~p q) ~r Use a truth table to determine whether the argument is valid or invalid. 22) If you are infected with the measles, then it can be transmitted. The results are grave and it cannot be transmitted. Therefore, if the results are not grave, then you are infected with the measles Use an Euler diagram to determine whether the syllogism is valid or invalid. 23) All businessmen wear suits. Aaron wears a suit. Aaron is a businessman. Decide whether the statement is true or false. 27) If a right angle is broken up into two new angles, these two new angles are also right. Find the requested angle. 28) Supplement of 29) If 1 and 2 are complementary angles and 1 is 4 times as large as 2, then what are the measures of the two angles? Classify the polygon by name. If it is a quadrilateral, give its specific name. 30) 24) Some TV shows are comedies. All comedies are hits. Some TV shows are hits.

3 Identify the quadrilateral. 31) The figures are similar. Find the length of the missing side indicated with an x. 35) Find the measure of x. 32) Double the length of each side of the given rectangle then find the area. 36) Find the requested measurement. Use π = 3.14 and round your answer to the nearest hundredth. 33) Find the circumference of the circle. Find the area of the shaded region in the figure. Round results to the nearest unit. Use π = ) Use the information below to answer the question. Note: lines and are parallel. 34) Find the measure of the angle indicated by x. 38)

4 Convert the following. 39) 92 F to C 40) 4 C to F 41) 13 lb to kg 42) 3T to ml 43) 48 fl oz to qt 44) 4 pt to L 45) 23 kg to mg 46) 2.83 m to cm 47) 11 yd 2 to square feet 48) 81 ft 2 to square yards 49) 7.4 m 3 to cubic centimeters 50) Below is a schematic depiction of a waterslide. The slide is 19 ft long. The ladder leading to the top of the slide is 16 ft long. How far is it from the end of the slide to the foot of the ladder? Round your answer to hundredths. 51) The shape of a patio is trapezoidal with a height of 9 ft and bases of 14 ft and What is the cost of outdoor carpeting to cover the patio if the carpeting costs $22.50 per yd 2? Find the volume of the solid. When appropriate, use π = 3.14 and round your answer to the nearest hundredth. 52) Find the volume of the shaded solid. Round your answer to 2 decimal places if necessary. 53) 54) Three people build a rectangular building 80 dm wide, 6 m long, and 7 m high. How many cubic meters does the shed contain? 55) How many ways can a committee of 5 be selected from a club with 10 members? 56) In how many ways can 4 people be chosen and arranged in a straight line, if there are 7 people from whom to choose? 57) License plates are made using 3 letters followed by 3 digits. How many plates can be made if repetition of letters and digits is allowed? 58) A license plate is to consist of 2 letters followed by 3 digits. Determine the number of different license plates possible if repetition of letters and numbers is not permitted.

5 Use the table to find the probability. 59) The table shows the number of college students who prefer a given pizza topping. 67) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the first card is a king and the second card is a queen. 68) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black. Determine the probability a student prefers meat topping given that the student is a junior. Answer the question. 60) How many different arrangements are there of the letters in the word "trouble"? 61) A class consists of 23 women and 83 men. If a student is randomly selected, what is the probability that the student is a woman? 62) A fair die is rolled. What is the probability of rolling a 3 or a 4? Find the probability. 63) A card is drawn at random from a wellshuffled deck of 52 cards. What is the probability of drawing a face card or a 3? 64) One card is selected from a deck of cards. Find the probability of selecting a diamond or a card less than 4. (Note: The ace is considered a low card.) 65) A bag contains 2 red marbles, 4 blue marbles, and 8 green marbles. What is the probability of choosing a marble that is not blue? 66) If you are dealt two cards successively (with replacement of the first) from a standard 52-card deck, find the probability of getting a heart on the first card and a diamond on the second. Identify the sampling technique used to obtain a sample. 69) A game warden chooses to check for fishing licenses in every 10th boat he encounters on his patrol. 70) In order to determine the expected number of broken eggs per carton, an egg packaging worker selects a group of 50 cartons that come off a particular conveyor belt and counts the number of broken eggs within these cartons. Use the data to construct a frequency distribution. 71) First Class = Be prepared to construct each of the following graphs. 72) 1) histogram 2) frequency polygon 3) stem-and-leaf plot Find the mean of the set of data. Round your answer to the nearest tenth. 73) 11, 16, 2, 2, 2, 5, 7, 7, 8 Find the median of the set of data. 74) 1, 7, 11, 26, 30, 39, 49 Find the mode or modes for the set of numbers. 75) 5, 9, 48, 3, 2, 8, 42, 1, 4, 16 Find the midrange of the set of data. 76) 9, 4, 3, 18, 4, 6, 23, 16, 16

6 77) To get a C in history, Nathan must have a mean of 72 on four tests. Scores on the first three tests were 69, 75, and 60. What is the lowest score that Nathan can get on the last test and still receive a C? Answer the question. 78) What percent of a data set lies below each of the following:,,, Find the range for the set of data given. 79) 7, 16, 3, 14, 12 Find the standard deviation. Round to one more place than the data. 80) 13, 8, 8, 18, 18, 6, 11, 10, 18 81) The average weekly income of teachers in one school district is $390 with a standard deviation of $45. Find the percentage of teachers earning more than $425 a week. 82) Assume that the mean length of a human pregnancy is 268 days with a standard deviation of 9 days. a) What percentage of human pregnancies do we expect to last 260 days or less? b) If you have a medical practice with 125 pregnant clients, how many deliveries could you expect in 260 days or less?

Use Venn diagrams to determine whether the following statements are equal for all sets A and B. 2) A' B', A B Answer: not equal

Test Prep Name Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z} Determine the following. ) (A' C) B' {r, t, v, w, x} Use Venn diagrams to determine whether